| Semester | Titel | Typ |
|---|---|---|
| Summer Semester 2013 | Geometric Numerical Integration | Lecture |
Relocated to University of Adelaide, Australia.
Please here click to be forwarded.
The key focus is on constructing probability distributions of jump Markov processes that arise in Biology. Solving the Chemical Master Equation (CME) is one method in which we can construct a pdf for such processes. Knowing the probability distribution gives vital information about the state the biological system is likely to be in and where it is likely to go. Computing accurate approximations of the CME is a difficult task when there are a variety of interactions in the biological process being modeled. I work in the following key research topics to tackle these problems and make the CME tractable:
Research Topics
- Domain selection techniques for high dimensional CME.
- Parallelisation of the CME for HPC.
- Hybrid methods to reduce complexity of the CME.
- Numerical methods for Stochastic processes in Biology.
PhD
Analysis and Numerics of the Chemical Master Equation
Supervised by Professor Markus Hegland at the Australian National University.
Talks in 2013
Title: Modern Numerical Methods for Continuous Time Markov Chains of High-Dimensions
Biomath 2013, Sofia Bulgaria June 16-21.
Publications
Vikram Sunkara, Markus Hegland
Parallelising the finite state projection method
ANZIAM Journal, 2011
Vikram Sunkara, Markus Hegland
An optimal finite state projection method
Procedia Computer Science, 2010 - Elsevier
Vikram Sunkara
The Chemical Master Equation With Respect To Reaction Counts
Proc. 18th World IMACS/MODSIM Congress, 2009
Preprints
Vikram Sunkara
Finite State Projection method for Hybrid Models.
Submitted 2013.
Tobias Jahnke and Vikram Sunkara.
Error bound for hybrid models of two-scaled stochastic reaction systems.
Submitted 2013.
Software
CMEPy is a python based FSP CME solver. The software was designed to adaptively select the domain to help compute an accurate approximation to the solution of large dimensional CME. There are key additions to this package which give very fast computation times, the algorithms are based on methods proposed in my thesis. The modules include:
- OFSP : Optimal support size selection for the FSP method.
- PFSP : Parallelisation of the CME problem onto HPC/Multi-core infrastructure.
- GORDE : A domain selector for high dimensional problems which guarantees the solutions accuracy A priori.
These modules will be released upon the completion of the examination process. If these additions are required earlier, please email me.